Spherical Harmonic Analysis of Gravitational Curvatures and Its Implications for Future Satellite Missions

In this study we assume that a gravitational curvature tensor, i.e. a tensor of third-order directional derivatives of the Earth’s gravitational potential, is observable at satellite altitudes. Such a tensor is composed of ten different components, i.e. gravitational curvatures, which may be combined into vertical–vertical–vertical, vertical–vertical–horizontal, vertical–horizontal–horizontal and horizontal–horizontal-horizontal gravitational curvatures. Firstly, we study spectral properties of the gravitational curvatures. Secondly, we derive new quadrature formulas for the spherical harmonic analysis of the four gravitational curvatures and provide their corresponding analytical error models. Thirdly, requirements for an instrument that would eventually observe gravitational curvatures by differential accelerometry are investigated. The results reveal that measuring third-order directional derivatives of the gravitational potential imposes very high requirements on the accuracy of deployed accelerometers which are beyond the limits of currently available sensors. For example, for orbital parameters and performance similar to those of the GOCE mission, observing third-order directional derivatives requires accelerometers with the noise level of \({\sim}10^{-17}\,\hbox {m}\,\hbox {s}^{-2}\) Hz\(^{-1/2}\).     

A defense of the theory of progressive soil salinization in ancient southern Mesopotamia

An explanation is given of the fundamental processes of soil salinization and degradation induced by irrigation of poorly-drained river valleys in arid regions, and of why these processes were practically uncontrollable under the circumstances of ancient Southern Mesopotamia.     

Spring water table depth mediates within-site variation of soil temperature in groundwater-fed mires

Groundwater-dependent ecosystems represent globally rare edaphic islands of scattered distribution, often forming areas of regionally unique environmental conditions. A stable groundwater supply is a key parameter defining their ecological specificity, promoting also soil thermal buffering. Still, a limited number of studies dealt with the importance of water temperature in mire ecosystems and virtually no data exist on within-site variation in the temperature buffer effect. Three temperature dataloggers, placed in patches potentially differing in groundwater supply, were installed in each of 19 Western Carpathian spring mire sites from May 2019 to July 2020. Spring source plots statistically differed in water temperature parameters from the plots located towards the spring mire margin, which did not significantly differ from one another. At the majority of sites, the temperature values changed gradually from spring source to mire margins, fitting the pattern expected in the groundwater temperature buffering scenario. Dataloggers placed in the spring sources were the most distinctive from the others in thermal buffering parameters in conditional principal component analysis. The difference between the spring source and its margin was on average 3.25 °C for 95th percentile of the recorded water temperature data points (i.e. warm extremes) and 1.91 °C for 5th percentile (i.e. cold extremes). This suggests that if the temperature at spring source area is considered, thermal buffering within a site may mitigate mainly warm extremes. Thus, our data may provide an important baseline for predictions of possibly upcoming changes in spring mire hydrology caused by climate change. Both warming and precipitation decrease can give rise to the loss or substantial reduction of buffering effect if the contrasting parameters now recorded at the central part shift to those found towards the margins of groundwater-fed areas.     

The Temperature – Magnetic Field Relation in Observed and Simulated Sunspots

Observations of the relation between continuum intensity and magnetic field strength in sunspots have been made for nearly five decades. This work presents full-Stokes measurements of the full-split (\(g = 3\)) line Fe i 1564.85 nm with a spatial resolution of \(0.5^{\prime\prime}\) obtained with the GREGOR Infrared Spectrograph in three large sunspots. The continuum intensity is corrected for instrumental scattered light, and the brightness temperature is calculated. Magnetic field strength and inclination are derived directly from the line split and the ratio of Stokes components. The continuum intensity (temperature) relations to the field strength are studied separately in the umbra, light bridges, and penumbra. The results are consistent with previous studies, and it was found that the scatter of values in the relations increases with increasing spatial resolution thanks to resolved fine structures. The observed relations show trends common for the umbra, light bridges, and the inner penumbra, while the outer penumbra has a weaker magnetic field than the inner penumbra at equal continuum intensities. This fact can be interpreted in terms of the interlocking comb magnetic structure of the penumbra. A comparison with data obtained from numerical simulations was made. The simulated data generally have a stronger magnetic field and a weaker continuum intensity than the observations, which may be explained by stray light and limited spatial resolution of the observations, and also by photometric inaccuracies of the simulations.     

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

The static Earth’s gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth’s surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet’s boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green’s kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.     

European glacial relict snails and plants: environmental context of their modern refugial occurrence in southern Siberia

Knowledge of present‐day communities and ecosystems resembling those reconstructed from the fossil record can help improve our understanding of historical distribution patterns and species composition of past communities. Here, we use a unique data set of 570 plots explored for vascular plant and 315 for land‐snail assemblages located along a 650‐km‐long transect running across a steep climatic gradient in the Russian Altai Mountains and their foothills in southern Siberia. We analysed climatic and habitat requirements of modern populations for eight land‐snail and 16 vascular plant species that are considered characteristic of the full‐glacial environment of central Europe based on (i) fossil evidence from loess deposits (snails) or (ii) refugial patterns of their modern distributions (plants). The analysis yielded consistent predictions of the full‐glacial central European climate derived from both snail and plant populations. We found that the distribution of these 24 species was limited to the areas with mean annual temperature varying from ?6.7 to 3.4 °C (median ?2.5 °C) and with total annual precipitation varying from 137 to 593 mm (median 283 mm). In both groups there were species limited to areas with colder and drier macroclimates (e.g. snails Columella columella and Pupilla loessica, and plants Kobresia myosuroides and Krascheninnikovia ceratoides), whereas other species preferred areas with relatively warmer and/or moister macroclimates (e.g. snails Pupilla turcmenica and P. alpicola, and plants Artemisia laciniata and Carex capillaris). Analysis of climatic conditions also indicated that distributional shifts of the studied species during the Pleistocene/Holocene transition were closely related to their climatic tolerances. Our results suggest that the habitat requirements of southern Siberian populations can provide realistic insights into the reconstruction of Eurasian, especially central European, glacial environments. Data obtained from modern populations also highlight the importance of wet habitats as refugia in the generally dry full‐glacial landscape.     

Automated calibration of advanced soil constitutive models. Part I: hypoplastic sand

Acta Geotechnica - This paper discusses an automated deterministic approach to parameters calibration of the hypoplastic model for sand. The calibration is performed on results from basic...     

Integrated geophysical and geological methods to investigate the inner and outer structures of the Quaternary Mýtina maar (W-Bohemia,Czech Republic)

The Mýtina maar is the first known Quaternary maar in the Bohemian Massif. Based on the results of Mrlina et al. (J Volcanol Geother Res 182:97–112, 2009), a multiparametric geophysical (electrical resistivity tomography, gravimetry, magnetometry, seismics) and geological/petrochemical research study had been carried out. The interpretation of the data has provided new information about the inner structure of the volcanic complex: (1) specification of the depth of post-volcanic sedimentary fill (up to ~100 m) and (2) magnetic and resistivity signs of one (or two) hidden volcanic structures interpreted as intrusions or remains of a scoria cone. The findings at the outer structure of the maar incorporate the (1) evidence of circular fracture zones outside the maar, (2) detection and distribution of volcanic ejecta and tephra-fall deposits at the surface, and (3) indications from electrical resistivity tomography and gravity data in the area between the Mýtina maar and ?elezná h?rka scoria cone, interpreted as a palaeovalley, filled by volcaniclastic rocks, and aligned along the strike line (NW–SE) of the Tachov fault zone. These findings are valuable contributions to extend the knowledge about structure of maar volcanoes in general. Because of ongoing active magmatic processes in the north-east part of the Cheb Basin (ca. 15–30 km north of the investigation area), the Mýtina maar-diatreme volcano and surroundings is a suitable key area for research directed to reconstruction of the palaeovolcanic evolution and assessment of possible future hazard potential in the Bohemian Massif.